Re: Simulating multiple correlated stochastic processes

Posted by Max-118 on
URL: http://quantlib.414.s1.nabble.com/Simulating-multiple-correlated-stochastic-processes-tp6488p6493.html

Hi Luigi,

I have just done some basic test on a basket call option on the average return of 4 assets (using Sobol Quasi-random number generator). And the correlation matrix given is positive semi-definite. The following compares the fair values produced by Cholesky and Spectral decompositions for different number of iterations. (see attached chart).

no. of trails    Cholesky       Spectral         relative difference
500               0.14439479    0.14822383    2.6518%
1000             0.14844382    0.15099720    1.7201%
3000             0.15228533    0.15291014    0.4103%
5000             0.15295908    0.15328304    0.2118%
7000             0.15288972    0.15356331    0.4406%
10000           0.15333001    0.15370840    0.2468%
15000           0.15339209    0.15373016    0.2204%
30000           0.15374863    0.15387913    0.0849%
60000           0.15390326    0.15396157    0.0379%
90000           0.15393888    0.15402227    0.0542%
120000         0.15395743    0.15402453    0.0436%
150000         0.15396883    0.15405399    0.0553%
200000         0.15399083    0.15405433    0.0412%
300000         0.15400569    0.15404896    0.0281%
600000         0.15403359    0.15405266    0.0124%


As you can see, the two methods converge at higher number iterations; and Spectral decomposition seems to have higher rate of convergence rate. Is this behavior expected? and any existing literature explains the difference between them?

Best regards,
Max

On Tue, Jul 1, 2008 at 6:46 PM, Luigi Ballabio <[hidden email]> wrote:

On Thu, 2008-06-26 at 01:28 +0800, Max wrote:
> Given correlation matrix is symmetric and positive semidefinite, can I
> use SalvagingAlgorithm::none method (which is essentially a Cholesky
> decomposition) instead?

Yes, you can.

> And in this case, would the final results be equivelant for
> SalvagingAlgorithm::Spectral and SalvagingAlgorithm::none methods?

It should be. It would be nice if you made the experiment and reported
back here...

Luigi


--

Ninety percent of everything is crap.
--- Theodore Sturgeon

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